The answer is B. Fabiana has completed the same amount of the course as Samantha because 6/15=8/20. Both fractions reduce to 2/5. Therefore, they are equivalent.
Answer:
Step-by-step explanation:
Both expressions are examples of the <em>distributive property</em>, which basically says "if I have <em>this </em>many groups of some size and <em>that</em> many groups of the same size, I've got <em>this </em>+ <em>that</em> groups of that size altogether."
To give an example, if I've got <em>3 groups of 5 </em>and <em>2 groups of 5</em>, I've got 3 + 2 = <em>5 groups of 5 </em>in total. I've attached a visual from Math with Bad Drawings to illustrate this idea.
Mathematically, we'd capture that last example with the equation
. We can also read that in reverse: 3 + 2 groups of 5 is the same as adding together 3 groups of 5 and 2 groups of 5; both directions get us 8 groups of 5. We can use this fact to rewrite the first expression like this: 
.
This idea extends to subtraction too: If we have 3 groups of 4 and we take away 1 group of 4, we'd expect to be left with 3 - 1 = 2 groups of 4, or in symbols: 
. When we start with two numbers like 15 and 10, our first question should be if we can split them up into groups of the same size. Obviously, you could make 15 groups of 1 and 10 groups of 1, but 15 is also the same as <em>3 groups of 5</em> and 10 is the same as <em>2 groups of 5</em>. Using the distributive property, we could write this as 
, so we can say that 
.
Hi. 2 (×+1)=3×-1 ; 2x+2= 3x-1 ;
2x-3x= -1-2 ; -x = -3 ; x=3. Hope this helps.
Since Christian sets aside $60 per month for daily coffee, and McDonalds sells coffee for $ 1, and The Bean Sprout sells a cup of coffee for $3, to create an equation that represents the combinations of coffee options that allow Christian to stay in his budget and provide 2 combinations that use his entire budget, 1 combination that would be under budget, and 1 combination that would be over his budget, the following linear equation must be proposed:
M + BS = 60
2 combinations using the entire budget =
- 15 McDonalds + 15 The Bean Sprout = 15 + 45 = 60
- 30 McDonalds + 10 The Bean Sprout = 30 + 30 = 60
1 combination under budget =
- 15 McDonalds + 10 The Bean Sprout = 15 + 30 = 45
1 combination over budget =
- 30 McDonalds + 30 The Bean Sprout = 30 + 90 = 120
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